One of the work-horses of econometric modelling is the Cochrane-Orcutt (1949) estimator, or some variant of it such as the Beach-MacKinnon (1978) full ML estimator. The C-O estimator was proposed by Cochrane and Orcutt as a modification to OLS estimation when the errors are autocorrelated. Those authors had in mind errors that follow an AR(1) process, but it is easily adapted for any AR process.

I've blogged elsewhere about the the historical setting for the work by Cochrane and Orcutt.

Given the limited computing power available at the time, the C-O estimator was a pragmatic solution to the problem of obtaining the GLS estimator of the regression coefficients, and approximating the full ML estimator. Students of econometrics will be familiar with the iterative process associated with the C-O estimator, as outlined below.

The use of this estimator leads to some interesting questions. Is this iterative scheme guaranteed to converge in a finite number of iterations? Is there a unique solution to this convergence problem, or can multiple local solutions (minima) occur?